We consider a \(3\times 3\)  km\(^2\)  urban area where a single UAV (or a TUAV or an iTUAV) is deployed to provide cellular coverage for terrestrial users equipment (UEs). The transmit power is set to \(P_t=30\)  dBm and the UE receiver sensitivity is \(P_{\min }=-70\)  dBm [1]}, which translates to a path loss threshold of 100 dB. We assume that the air-to-ground channels follow the probabilistic line-of-sight (LoS) and non-LoS (NLoS) propagation model [2]}, operating at frequency \(f_c=2\)  GHz. The average height of anchors is 50 m and the maximal tether length for both the TUAV and iTUAV is set to 150 m [3]}. For the sake of simplicity, we assume that the TUAV (resp. iTUAV) minimum inclination angle that prevents tangling around surrounding buildings and ensures the safety of the tether is set to 0\(^\circ \) . The UEs are distributed according to the Thomas point process. With this distribution, clustering of UEs is modeled through the coefficient of variation (CoV) of the Voronoi cell area around each user [4]}. For instance, when \(\text{CoV}=1\) , the UEs are uniformly distributed according to the Poisson point process, whereas a higher CoV represents more clustered users around a virtual cluster head. At each realization, i.e., UEs and anchors geographical distributions, the iTUAV determines the optimal anchor and attaches to it to provide cellular coverage to the highest number of UEs. In contrast, the untethered UAV freely determines and reaches the optimal 3D location that maximizes its coverage [1]}, whereas the TUAV, constrained to its pseudo-static deployment, relocates withing its hovering region to cover the maximal number of UEs [3]}. Finally, results are averaged over both the UEs' geographical distribution and anchor positions in each iteration.
